I agree with Duc Ton Vinh Lam. I bet he lives in the north of Vietnam so he knows there quite well.
If you want to experience sth traditional, you should spend 2 or 3 days in Ha Noi on visiting Ha Noi old quarter, trying local food, visting old constructions built at feudal periods. Ha Long Bay is great, but I wasnt interested in staying there for so long because there arent so many activities to do.
Warning: except in Hanoi, don't buy accesorries made from pearl or jewel, even if they offer you a discount!
Then you can go to Da Nang, a nice city along the sea. It's a city of bridges. I'm said, Da Nang's beaches are great and secure. [However, I have never been there. Vung Tau beach - a coastal place near HCM city- is more popular for me. So I suggest you do searching about Da Nang]
HCM city is quite young, mordern. Some constructions bearing the stamp of France colonist: Saigon Notre-Dame Basilica, Saigon Central Post Office, War Remnants Museum... may interest you. HCM-er likes coffee. We have a cutural habit of enjoying coffee. I think it just takes you 2 days there.
My English teacher from Chicago is quite amazed by the beauty of Mekong Delta's provinces. Its life hier is very Vietnam, with local markets on rivers, rice fields, tropical fruits' gardens...
Warning: there is a local dish call "mắm". It has smell and is strange for foreigners, so please dont try to taste it!